Microcantilevers containing a microchannel can enable precise resonance-based measurement of very small masses entrained in a fluid flowing through the microchannel. Burg et al. describe one such system based on the principle that “the resonance frequency of a suspended microfluidic channel . . . is highly sensitive to the presence of molecules or particles whose mass density differs from that of the [fluid].” (Burg, Thomas P.; Godin, Michel; Knudsen, Scott M.; Shen, Wenjiang; Carlson, Greg; Foster, John S.; Babcock, Ken; Manalis, Scott R. “Weighing of biomolecules, single cells and single nanoparticles in fluid,” Nature, 446, 1066-1069 (Apr. 26, 2007)).
FIG. 1A shows a schematic representation 100a of a microcantilever 110 with a microchannel 120 according to the prior art. A thin (e.g., with thickness O[μm]) silicon microcantilever 110 extends outward from an essentially rigid base 130 into a cavity 190. As illustrated by the arrows indicating the direction of flow, a U-shaped microchannel 120 (e.g., with thickness and depth O[μm]) etched in the silicon transports a fluid outward from the rigid base 130 and into the body of the microcantilever 110 before returning the fluid to the rigid base 130. The free end 140 of the microcantilever 110 readily flexes in and out of the plane of FIG. 1A. Using an electrostatic drive electrode (not shown) driven by a gain controlled oscillator circuit, it is possible to excite the microcantilever 110 within a vacuum cavity to determine its characteristic resonance frequency.
FIG. 19 shows an isometric view 100b of a microcantilever 110 as schematically represented in FIG. 1a. FIG. 1B is provided to illustrate how a microcantilever 110 may be configured to extend outward from a rigid base 130 into a cavity 190.
FIG. 1C shows a first technique 100c for measuring small masses using a microcantilever 110 with a microchannel 120 according to the prior art. In this approach, the resonance frequency of the microcantilever 110 is monitored continuously as fluid flowing through the microchannel 120 conveys discrete sample particles 150a-c toward and away from the tip 140 of the microcantilever 110. Provided that the concentration of the particles 150a-c within the fluid is relatively sparse (i.e. it is relatively unlikely that two particles will simultaneously flow along the length of microchannel 120 within the microcantilever 110), the resonance frequency will vary according to the following equation:
                    f        =                              1                          2              ⁢                                                          ⁢              π                                ⁢                                    k                                                m                  _                                +                                  α                  ⁢                                                                          ⁢                  m                                                                                        Equation        ⁢                                  ⁢                  (          1          )                    where k is the spring constant of the microcantilever 110, m is the effective mass of the microcantilever 110 and any fluid therein, in is the mass of an individual sample particle 150a-c, and a is a geometric constant reflecting the current location of the sample particle 150a-c. When an individual particle 150a-c is near the tip 140 of the microcantilever 110, α≈1. When an individual particle 150a-c is near the rigid base 130 of the microcantilever 110 (or when no particles are within the length of the microchannel 120 within the microcantilever 110), α≈0. Thus, by observing the peak-to-trough differences in the resonance frequency as it varies over time, it is possible to determine the mass of an individual sample particle 150a-c as it flows past the tip 140 of the microcantilever 110.
FIG. 1D shows a second technique 100d for measuring small masses using a microcantilever 110 with a microchannel 120 according to the prior art. In this approach, an agent 160 that will bind the sample particles is immobilized against the interior walls of the microchannel prior to testing. Fluid containing sample particles is then flowed through the microchannel 120 and a single layer of sample particles adheres to the binding agent 160. A subsequent resonance measurement allows the mass of the layer of sample particles to be determined from Equation 1. However, in this approach, m includes the mass of the binding agent 160, and a value of α≈0.25 reflects the approximately uniform distribution of the sample particle layer along the length of the microcantilever 110.
The above two approaches do provide high measurement sensitivity, resolving masses as small as 300×10−18 g. However, both approaches are only applicable to sample particles that can be conveyed by the fluid flowing through the microchannel. The above two approaches are thus not well suited, for example, to measurement of biological particles that must be grown on a mechanical substrate that is too large or too fragile to be conveyed through the microchannel.